Ginsburg said the chief justice’s “life experience” had played a part in the shift. One of his daughters was a recently divorced mother with a demanding job. Her explanation, though widely accepted, was but informed speculation. Now there is data to go with the intuition. It turns out that judges with daughters are more likely to vote in favor of women’s rights than ones with only sons. The effect, a new study found, is most pronounced among male judges appointed by Republican presidents, like Rehnquist.

“Our basic finding is quite startling,” said Maya Sen, a political scientist at the University of Rochester (N.Y.) who conducted the study with Adam Glynn, a Harvard government professor.

The standard scholarly debate about how judges decide cases tends to revolve around two factors: law and ideology. “Here, we’ve found evidence that there is a third factor that matters: personal experiences,” Sen said. “Things like having daughters can actually fundamentally change how people view the world, and this, in turn, affects how they decide cases.”

The new study considered some 2,500 votes by 224 federal appeals court judges. “Having at least one daughter,” it concluded, “corresponds to a 7 percent increase in the proportion of cases in which a judge will vote in a feminist direction.”

Additional daughters do not seem to matter. But the effect of having a daughter is even larger when you limit the comparison to judges with only one child. “Having one daughter as opposed to one son,” the study found, “is linked to an even higher 16 percent increase in the proportion of gender-related cases decided in a feminist direction.”

The authors also looked at the same judges’ votes in a separate set of 3,000 randomly chosen cases. There was no relationship between having daughters and liberal votes generally. Daughters made a difference in only “civil cases having a gendered dimension.”

Researchers have found similar “daughter effects” in other areas. Members of Congress with daughters are more likely to cast liberal votes, particularly on abortion rights, one study found. Another study showed that British parents with daughters were more likely to vote for left-wing parties, while ones with sons were more likely to vote for right-wing parties.

The study on judges considered some explanations. Perhaps judges wanted to shield their daughters from harm. But the voting trends showed up in only civil cases, like ones involving claims of employment discrimination, and not criminal ones, including rape and sexual assault.

The most likely explanation, Sen said, was the one offered by Ginsburg. “By having at least one daughter,” she said, “judges learn about what it’s like to be a woman, perhaps a young woman, who might have to deal with issues like equity in terms of pay, university admissions or taking care of children.”